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独孤九剑

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  • TA的每日心情
    郁闷
    2012-4-30 23:06
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      “独孤九剑”的要旨,在于一眼见到对方招式中的破绽,便即乘虚而入,后发先至,一招制胜,

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    1#
    发表于 2009-2-2 22:25 |只看该作者 |倒序浏览
    |招呼Ta 关注Ta
    Group # y4 ^4 F$ w1 J' B" Z8 c4 R% r8 ]
    A group is defined as a finite or infinite set of Operands/ U) W2 Y+ }# `. _* G( _! R, {
    (called ``elements'') , , , ... that may be combined or ``multiplied'' via a Binary Operator) n& Y5 e# Q0 G7 r5 r0 w. b4 ~  \/ x
    to form well-defined products and which furthermore satisfy the following conditions:
    0 a) D7 ^5 F, I  g) C1. Closure: If and are two elements in , then the product is also in . 1 Z* _( {; K5 z+ T+ I+ q2 N3 r6 B
    2. Associativity: The defined multiplication is associative, i.e., for all , .   A% S/ z2 w6 d# |5 o" {3 @
    3. Identity: There is an Identity Element
    5 U2 @) D) \( q  Q (a.k.a. , , or ) such that for every element . ; l$ S6 e! U; n1 g7 W
    4. Inverse: There must be an inverse or reciprocal of each element. Therefore, the set must contain an element such that for each element of .
    ! v9 g% c1 t- q2 [A group is therefore a Monoid9 ^- z4 L* x6 r! i: ^+ ^+ h! [
    for which every element is invertible. A group must contain at least one element. 0 R0 Z* c- D, r; S  K9 n" ^

    4 i' J: F0 J7 _# a% W$ z, ^! hThe study of groups is known as Group Theory
    3 t6 h9 g0 q+ y. p% p. If there are a finite number of elements, the group is called a Finite Group
    0 l& c3 ]' Z! h* A7 p( ` and the number of elements is called the Order, R% b- U3 q; c% D$ f3 X; k0 ]
    of the group. 9 n% V5 J4 A2 a" K

    8 a9 F+ a  h; s. M3 y- ~6 DSince each element , , , ..., , and is a member of the group, group property 1 requires that the product
    ! @+ E. P0 G' J3 ]
    ) J' C4 R8 g! A2 H1 M4 E
    (1)5 I  l3 r8 |7 Q/ M+ ?; B. d; v# E  u/ }
    + v& d( H) s; N7 U
    4 }- G# x7 t) ?. l9 S$ Q3 B

    0 z8 P6 p* a, C+ q) Omust also be a member. Now apply to ,
    % O9 D0 G0 m& J7 n" z
    + Q) T7 k" Y: p
    # s! v: v+ C* `# W  v* D
    (2)
    9 t" \* r! [7 a$ z3 `* ]" Y
    " V$ A6 G6 A- U1 B  g9 {  l
    / q. s# J+ v) B8 j5 E

    ; \5 y$ v2 A, X% f1 V0 U$ L. OBut
    9 u& Y5 V% p: o
    9 q* O5 H: g/ H

    ) k& S" F" }3 @. g% {
    + Q; S$ {* v  |4 n; C7 E
    $ ~, Z' N& B0 ~4 J7 Q9 e

    : }0 j* F- E* R: h
    (3)4 r! }: D7 H4 i6 l
    so
    ) e8 F7 v) |' a+ n2 C

    5 z2 O4 Z! ^4 _5 s8 T
    (4)1 d% z- J- M/ U( j

    6 s* o1 ~1 J* K0 b4 `
    5 S9 z" I/ {* C1 C/ R" [. _  n' o- Q; A; z7 o
    which means that % m& \) x! o# ~& U* p3 a8 Z
    1 v& d6 Y& v" i: U: m1 x: Y
    (5)
    ' J7 f: h- z0 j+ R) ]
    - s% [/ a3 v0 p3 J% v/ I: I

    2 L# d: B& T; J2 x5 d+ U2 ^5 \# z$ o6 x$ M: Q3 c( }1 @: j1 ?
    and " ?6 N& {1 B  e! j) r0 |
    " z" {0 s" V7 G! U* Y( R# k
    (6)" A9 D  t. x" Q  f8 S- m: f4 h9 z

    ) e! d1 ^  e1 c& f& f
    7 |  S9 H9 K1 y8 H5 g' L0 R4 m( q# Z- K8 l. J
    , ]1 P! ]2 l9 o" q

    ! D+ ^* K$ C: k
    zan
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    OLS 实名认证       

    60

    主题

    6

    听众

    1594

    积分

    独孤九剑

    升级  59.4%

  • TA的每日心情
    郁闷
    2012-4-30 23:06
  • 签到天数: 6 天

    [LV.2]偶尔看看I

    自我介绍


      “独孤九剑”的要旨,在于一眼见到对方招式中的破绽,便即乘虚而入,后发先至,一招制胜,

    新人进步奖

    群组南京邮电大学数模协会

    群组数学散仙

    群组数模应用

    群组数学趣味、游戏、IQ等

    群组2011年第一期数学建模

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